NSW Education Minister Rob Stokes said he is "furious" and has ordered an investigation after several students at Coonamble High School discovered that they have been taught the wrong maths course since the beginning of the year.
Two year 12 students and five year 11 students were being taught the mathematics general 1 syllabus instead of the higher-level mathematics general 2 course they elected.
Mr Stokes said the solutions being offered to the students are "not acceptable" and a spokesman for the NSW Department of Education said it has launched a "thorough investigation" of the incident.
"One of the solutions offered was if they don't do well they can do it again next year," Mr Stokes told 2GB Radio on Wednesday.
"That's clearly a laughable solution ... I'm angry on their behalf, if this was my child I would be furious.
"What the school has come up with, in my view, is not acceptable."
The error was discovered less than two months before the start of HSC exams on October 16 and the students have been told that they will be given "comprehensive support" to sit this year's mathematics general 2 exam.
A spokeswoman for the NSW Education Standards Authority said it was "sending the maths inspector to the school to work ... on what support and targeted teaching is needed".
"Support will focus on each student's individual situation," a spokesman for the Department of Education said.
All seven students had elected to study a compressed course, in which they complete both the preliminary and HSC course for some subjects in one year.
The error has implications for the students' HSC and ATAR eligibility as the general 1 course is non-examinable and does not count towards the minimum of six units students must study to be eligible for their HSC award or the 10 units required to calculate their ATAR.
Mathematics general 2, the course the students elected, is a two-unit course that counts towards both the HSC award and ATAR requirements and provides a foundation for a range of university courses and vocational pathways.
"There will be a thorough investigation of the circumstances, including the roles of staff with responsibilities for teaching and HSC procedures," the department's spokesman said.
"The school and the department is working actively with the NSW Education Standards Authority (NESA) to support students and assist in its investigation.
"As soon as the executive principal identified that the correct mathematics course was not being taught, her immediate priority has been to provide comprehensive support to students."